Expression of type Conditional

from the theory of proveit.core_expr_types.tuples

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, i, j, k, l
from proveit.core_expr_types import merge_equiv
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Natural, one, subtract

# build up the expression from sub-expressions
expr = Conditional(merge_equiv, And(InSet(subtract(k, i), Natural), InSet(subtract(l, j), Natural), Equals(k, Add(j, one))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\begin{array}{c} \begin{array}{l} \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right),f\left(k\right), f\left(k + 1\right), \ldots, f\left(l\right)\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(l\right)\right) \end{array} \end{array} \textrm{ if } \left(k - i\right) \in \mathbb{N} ,  \left(l - j\right) \in \mathbb{N} ,  k = \left(j + 1\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 17 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10
6	ExprTuple	11, 12
7	ExprTuple	13
8	Operation	operator: 15 operands: 14
9	Operation	operator: 15 operands: 16
10	Operation	operator: 17 operands: 18
11	ExprRange	lambda_map: 19 start_index: 40 end_index: 41
12	ExprRange	lambda_map: 19 start_index: 31 end_index: 33
13	ExprRange	lambda_map: 19 start_index: 40 end_index: 33
14	ExprTuple	20, 22
15	Literal
16	ExprTuple	21, 22
17	Literal
18	ExprTuple	31, 23
19	Lambda	parameter: 36 body: 24
20	Operation	operator: 27 operands: 25
21	Operation	operator: 27 operands: 26
22	Literal
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operand: 36
25	ExprTuple	31, 32
26	ExprTuple	33, 34
27	Literal
28	ExprTuple	41, 35
29	Variable
30	ExprTuple	36
31	Variable
32	Operation	operator: 38 operand: 40
33	Variable
34	Operation	operator: 38 operand: 41
35	Literal
36	Variable
37	ExprTuple	40
38	Literal
39	ExprTuple	41
40	Variable
41	Variable